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BV solutions and viscosity approximations of rate-independent systems

Alexander Mielke, Riccarda Rossi, Giuseppe Savaré (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In the nonconvex case, solutions of rate-independent systems may develop jumps as a function of time. To model such jumps, we adopt the philosophy that rate-independence should be considered as limit of systems with smaller and smaller viscosity. For the finite-dimensional case we study the vanishing-viscosity limit of doubly nonlinear equations given in terms of a differentiable energy functional and a dissipation potential that is a viscous regularization of a given rate-independent dissipation...

BV solutions and viscosity approximations of rate-independent systems∗

Alexander Mielke, Riccarda Rossi, Giuseppe Savaré (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In the nonconvex case, solutions of rate-independent systems may develop jumps as a function of time. To model such jumps, we adopt the philosophy that rate-independence should be considered as limit of systems with smaller and smaller viscosity. For the finite-dimensional case we study the vanishing-viscosity limit of doubly nonlinear equations given in terms of a differentiable energy functional and a dissipation potential that is a viscous regularization...

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